First of all this has been working just fine for a long time (I've had my watch for 1.5 years now). But recently (I think this past week) - my past weekly goals are not showing correctly on Garmin Connect. It has been correct before (this past week or so). It is showing much more activities miles (in my case Running) that what I had for that 7 day period. I have set up weekly goals starting on Sundays. For the days/week of 4/7/2019 - 4/13/2019, I should have 14.95 running miles logged (not the 25.27 miles that it is showing). I haven't changed any setting on my phone app nor connect so i'm not sure why this is all of a sudden reporting past goals incorrectly. (I have tried to upload screenshots, but to no avail...this forum message will not let me upload attachments for some reason!)
I noticed the same thing. I had a 35 km goal set up to span the April 29-May 5 dates. I did the math by hand, and it turns out that I ran 31.14 km in those days, but the goal shows 39.36 km. After a quick investigation I realized that the goal included today's (May 6) 8.22 km run, which should not be counted toward the goal. So yes, there's something broken (again) in Garmin Connect.
I did another run on May 6 and it, too, added up to the past goal that ended on May 5. The run was also included in the current goal that started May 6.
So it looks like goals continue to accumulate activities one day past its defined end time, even though the goal is already showing in the "Past goals" tab.
